where \(Z^{r}_{p,q}  \lbrace  a \in F_p C_k \mid d(c) \in F_{p-r} C_{k-1} \rbrace \) ,
and with the differentials \(d^r_{p,q}\)  induced by the differential \(d\)  of \(C_*\) . One can easily observe that \(E^0_{p,q} \cong F_p C_k / F_{p-1} C_{k}\)  and \(E^1_{p,q} \cong H_k (F_p C_* / F_{p-1} C_{*})\) , for all \(p,q\in \mathbb {Z}\) . The following classical result (see for example [1]}) describes the convergence of the spectral sequence to \(H_* (C_*)\)  under assumptions that are always verified in this article.
